We present results from the search for a stochastic gravitational-wave background (GWB) as predicted by the theory of General Relativity using six radio millisecond pulsars from the Data Release 2 (DR2) of the European Pulsar Timing Array (EPTA) covering a timespan up to 24 yr. A GWB manifests itself as a long-term low-frequency stochastic signal common to all pulsars, a common red signal (CRS), with the characteristic Hellings-Downs (HD) spatial correlation. Our analysis is performed with two independent pipelines, ENTERPRISE, and TEMPONEST+FORTYTWO, which produce consistent results. A search for a CRS with simultaneous estimation of its spatial correlations yields spectral properties compatible with theoretical GWB predictions, but does not result in the required measurement of the HD correlation, as required for GWB detection. Further Bayesian model comparison between different types of CRSs, including a GWB, finds the most favoured model to be the common uncorrelated red noise described by a power law with $A = 5.13_{-2.73}^{+4.20} \times 10^{-15}$ and $\gamma = 3.78_{-0.59}^{+0.69}$ (95 per cent credible regions). Fixing the spectral index to γ = 13/3 as expected from the GWB by circular, inspiralling supermassive black hole binaries results in an amplitude of $A =2.95_{-0.72}^{+0.89} \times 10^{-15}$. We implement three different models, BAYESEPHEM, LINIMOSS, and EPHEMGP, to address possible Solar system ephemeris (SSE) systematics and conclude that our results may only marginally depend on these effects. This work builds on the methods and models from the studies on the EPTA DR1. We show that under the same analysis framework the results remain consistent after the data set extension.

No abstract

Summary Model updating based on vibration response measurements is a technique for reducing inherent modeling errors in finite element (FE) models that arise from simplifications, idealized connections, and uncertainties with regard to material properties. Updated FE models, which have relatively fewer discrepancies with their real structural counterparts, provide more in‐depth predictions of the dynamic behaviors of those structures for future analysis. In this study, we develop a full‐scale FE model of a major long‐span bridge and update the model to improve an agreement between the identified modal properties of the real measured data and those from the FE model using a Bayesian model updating scheme. Sensitivity‐based cluster analysis is performed to determine robust and efficient updating parameters, which include physical parameters having similar effects on targeted natural frequencies. The hybrid Monte Carlo method, one of the Markov chain Monte Carlo sampling methods, is used to obtain the posterior probability distributions of the updating parameters. Finally, the uncertainties of the updated parameters and the variability of the FE model's modal properties are evaluated.

No abstract

The European Pulsar Timing Array (EPTA) collaboration has recently released an extended data set for six pulsars (DR2) and reported evidence for a common red noise signal. Here we present a noise analysis for each of the six pulsars. We consider several types of noise: (i) radio frequency independent, ‘achromatic’, and time-correlated red noise; (ii) variations of dispersion measure and scattering; (iii) system and band noise; and (iv) deterministic signals (other than gravitational waves) that could be present in the PTA data. We perform Bayesian model selection to find the optimal combination of noise components for each pulsar. Using these custom models we revisit the presence of the common uncorrelated red noise signal previously reported in the EPTA DR2 and show that the data still supports it with a high statistical significance. Next, we confirm that there is no preference for or against the Hellings–Downs spatial correlations expected for the stochastic gravitational-wave background. The main conclusion of the EPTA DR2 paper remains unchanged despite a very significant change in the noise model of each pulsar. However, modelling the noise is essential for the robust detection of gravitational waves and its impact could be significant when analysing the next EPTA data release, which will include a larger number of pulsars and more precise measurements.

Finite element model updating seeks to modify a structural model to reduce discrepancies between predicted and measured data, often from vibration studies. An updated model provides more accurate prediction of structural behavior in future analyses. Sensitivity-based parameter clustering and regularization are two techniques used to improve model updating solutions, particularly for high-dimensional parameter spaces and ill-posed updating problems. In this paper, a novel parameter clustering scheme is proposed which considers the structure of the objective function to facilitate simultaneous updating of disparate data, such as natural frequencies and mode shapes. In a small-scale updating example with simulated data, the proposed clustering scheme is shown to provide moderate to excellent improvement over existing parameter clustering methods, depending on the accuracy of initial model. A full-scale updating example on a large suspension bridge shows similar improvement using the proposed parametrization scheme. Levenberg-Marquardt minimization with Bayesian regularization is also implemented, providing an optimal regularized solution and insight into parametrization efficiency.

The International Pulsar Timing Array 2nd data release is the combination of datasets from worldwide collaborations. In this study, we search for continuous waves: gravitational wave signals produced by individual supermassive black hole binaries in the local universe. We consider binaries on circular orbits and neglect the evolution of orbital frequency over the observational span. We find no evidence for such signals and set sky averaged 95% upper limits on their amplitude h95. The most sensitive frequency is 10nHz with h95 = 9.1 × 10−15. We achieved the best upper limit to date at low and high frequencies of the PTA band thanks to improved effective cadence of observations. In our analysis, we have taken into account the recently discovered common red noise process, which has an impact at low frequencies. We also find that the peculiar noise features present in some pulsars data must be taken into account to reduce the false alarm. We show that using custom noise models is essential in searching for continuous gravitational wave signals and setting the upper limit.

No abstract